How to select two individual points without selecting other edges?
Select Mouse, i.e. the mouse button used for selection (see User Preferences), will call the Activate/Select operator which, by default, selects one vertex while deselecting the rest.

Shift + Select Mouse will call Activate/Select and toggle selection of vertices instead of deselecting other vertices, allowing you to multi-select individual vertices.

If a path of vertices is being selected when you attempt to multi-select, you're using Ctrl + Select Mouse which calls Pick Shortest Path, the operator that selects all vertices in a path between two individual vertices.